Problem: Which of the following numbers is a multiple of 12? ${45,68,74,80,108}$
Solution: The multiples of $12$ are $12$ $24$ $36$ $48$ ..... In general, any number that leaves no remainder when divided by $12$ is considered a multiple of $12$ We can start by dividing each of our answer choices by $12$ $45 \div 12 = 3\text{ R }9$ $68 \div 12 = 5\text{ R }8$ $74 \div 12 = 6\text{ R }2$ $80 \div 12 = 6\text{ R }8$ $108 \div 12 = 9$ The only answer choice that leaves no remainder after the division is $108$ $ 9$ $12$ $108$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $12$ are contained within the prime factors of $108$ $108 = 2\times2\times3\times3\times3 12 = 2\times2\times3$ Therefore the only multiple of $12$ out of our choices is $108$. We can say that $108$ is divisible by $12$.